Sheet 4

This sheet covers the material of lectures 13-16, with the topics manifolds with boundary, Stokes' Theorem, the degree of smooth maps, Riemannian metrics, isometries, and Killing fields. The relevant parts of the Hitchin lecture notes are Sections 7-9, and of the Lotay lecture notes Sections 6-8.

This sheet will not be marked, so please do not hand in solutions. The file 25C33Sheet4.pdf just contains the questions, whilst the file 25C33Soln4A+C.pdf contains the questions and the solutions to Sections A and C, and the file 25C33Soln4B.pdf contains the questions and the solutions to Section B.